Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1058–1069 | Cite as

Optimal credibility estimation of random parameters in hierarchical random effect linear model

  • Limin WenEmail author
  • Jing Fang
  • Guoping Mei
  • Xianyi Wu


In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.


Bayes theory credibility estimator hierarchical linear model random effect 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Limin Wen
    • 1
    • 2
    Email author
  • Jing Fang
    • 1
  • Guoping Mei
    • 1
    • 2
  • Xianyi Wu
    • 3
  1. 1.School of Mathematics and Information ScienceJiangxi Normal UniversityNanchangChina
  2. 2.School of Information ManagementJiangxi University of Finance and EconomicsNanchangChina
  3. 3.Department of Statistics and Actuarial ScienceEast China Normal UniversityShanghaiChina

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